By Ching H. Yew, Xiaowei Weng
Revised to incorporate present parts thought of for today’s unconventional and multi-fracture grids, Mechanics of Hydraulic Fracturing, moment variation explains the most very important good points for fracture layout — the facility to foretell the geometry and features of the hydraulically precipitated fracture. With two-thirds of the world’s oil and common fuel reserves dedicated to unconventional assets, hydraulic fracturing is the easiest confirmed good stimulation option to extract those assets from their extra distant and intricate reservoirs. besides the fact that, few hydraulic fracture versions can thoroughly simulate extra advanced fractures. Engineers and good designers needs to comprehend the underlying mechanics of the way fractures are modeled so that it will effectively are expecting and forecast a extra complicated fracture network.
Updated to deal with today’s fracturing jobs, Mechanics of Hydraulic Fracturing, moment version allows the engineer to:
Understand advanced fracture networks to maximise crowning glory strategiesRecognize and compute rigidity shadow, that may tremendously impact fracture community patternsOptimize completions by way of correctly modeling and extra safely predicting for today’s hydraulic fracturing completions
Discusses the underlying mechanics of making a fracture from the wellbore more advantageous to incorporate more moderen modeling elements comparable to pressure shadow and interplay of hydraulic fracture with a normal fracture, which aids in additional complicated fracture networksUpdated experimental experiences that follow to today’s unconventional fracturing cases.
Table of contents :
Front topic, Pages i-ii
Copyright, web page iv
Preface to the 1st version, Pages vii-viii
Preface to the second one version, web page ix
Chapter 1 - Fracturing of a wellbore and 2nd fracture versions, Pages 1-22
Chapter 2 - three-d fracture modeling, Pages 23-48
Chapter three - Proppant shipping in a 3D fracture, Pages 49-68
Chapter four - Deviated wellbores, Pages 69-88
Chapter five - Link-up of mini-fractures from perforated holes, Pages 89-103
Chapter 6 - Turning of fracture from a deviated wellbore, Pages 105-131
Chapter 7 - Fracture propagation in a obviously fractured formation, Pages 133-175
Chapter eight - pressure shadow, Pages 177-196
Chapter nine - Experimental stories, Pages 197-220
Notations, Pages 221-222
Author Index, Pages 223-226
Subject Index, Pages 227-234
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Revised to incorporate present elements thought of for today’s unconventional and multi-fracture grids, Mechanics of Hydraulic Fracturing, moment variation explains some of the most vital positive aspects for fracture layout — the facility to foretell the geometry and features of the hydraulically caused fracture.
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F. Carey, Grid Generation, Refinement and Redistribution, Wiley, UK, 1994. W. T. Houlsby, An implementation of Watson’s algorithm for computing twodimensional delaunay triangulations, Advancement in Engineering Softwares 6 (no. 4) (1984) 41–48. B. B. K. H. Klein, E. Siebrits, X. Dang, Layered Modulus Effects on Fracture Propagation, Proppant Placement, and Fracture Modeling, in: Paper SPE 71654, presented at SPE ATCE, New Orleans, 30 September–3 October, 2001. P. Peirce, E. Siebrits, The scaled flexibility matrix method for the efficient solution boundary value problems in 2D and 3D layered elastic media, Computer Methods in Applied Mechanics and Engineering 190 (no.
Note that when this time increment is used in solving Eq. (2-29), the condition of global volume conservation is automatically satisfied. Procedure for solving eqs. (2-24) and (2-29) These equations are solved by applying Picard iterative method as follows: (nÀ1) 1. An initial value of w(n) applied on the fraco is obtained by solving Eq. (2-14) with pressure p (n) , a successive p is solved from Eq. (2-29). A new w(n) ture surface On. Using this initial w(n) o 1 1 is then obtained by solving Eq.
This is done by calculating the Jacobians of the triangles formed by linking the new node and vertices of an old element. If the Jacobian is positive, the node is inside or on the side of the element; otherwise, the node is outside the element. The next step is to calculate the local coordinate (z, ) of the node from its global coordinate (x, y). For triangular elements, coordinate (z, ) can be calculated directly from the shape function to give 1 ½ðy À y1 Þðx À x1 Þ À ðx3 À x1 Þðy À y1 Þ, jJ j 3 1 ¼ ½Àðy2 À y1 Þðx À x1 Þ À ðx2 À x1 Þðy À y1 Þ, jJ j z¼ (2-44) jJ j ¼ ðx2 À x1 Þðy3 À y1 Þ À ðx3 À x1 Þðy2 À y1 Þ For bilinear elements, the functional relationship between (z, ) and (x, y) is nonlinear and implicit in z and as follows: 1 x ¼ ½ð1 À zÞð1 À Þx1 þ zð1 À Þx2 þ zð1 þ Þx3 þ ð1 À zÞð1 þ Þx4 2 1 y ¼ ½ð1 À zÞð1 À Þy1 þ zð1 À Þy2 þ zð1 þ Þy3 þ ð1 À zÞð1 þ Þy4 2 (2-45) The above equations are solved by applying Newton-Raphson iteration procedure.